Question

Starting from $x_0=1$, one step of Newton-Raphson method in solving the equation $2x^3+5x-8=0$ gives the next value $\left(x_1\right)$ as

• A. $\frac{5}{6}$
• B. $\frac{11}{12}$
• C. $\frac{6}{3}$
• D. $\frac{12}{11}$

Answer 1

The correct option is D $\frac{12}{11}$

According to Newton-Raphson method.
$x_1=x_0-\frac{f\left(x_0\right)}{f^{\prime }\left(x_0\right)}$
Given function $f\left(x\right)=2x^3+5x-8$
$f^{\prime }\left(x\right)=6x^2+5$
Given value of $x_0=1$
$f\left(x_0\right)=f\left(1\right)=2+5-8=-1$
$f^{\prime }\left(x_0\right)=f^{\prime }\left(1\right)=6+5=11$
$x_1=1+\frac{1}{11}=\frac{12}{11}$